A property deducible from the generic initial ideal

Abstract

Let S d be the vector space of monomials of degree d in the variables x 1,…, x s . For a subspace V ⊆ S d which is in general coordinates, consider the subspace gin( V) ⊆ S d generated by initial monomials of polynomials in V for the revlex order. We address the question of what properties of V may be deduced from gin( V). This is an approach for understanding what algebraic or geometric properties of a homogeneous ideal I ⊆ k[ x 1,…, x s ] that may be deduced from its generic initial ideal gin( I).